# Talk:Matching pursuit

This a review of "Matching Pursuit" for Scholarpedia, the article is written by Piotr J. Durka.

I will go over some omissions, minor mistakes, give some suggestions, etc.

1) I suggest to intorduce a symbol, say \mathcal{D}, for a generic dictionary earlier on the paper,
2) The meaning of abreviations such as EEG/MEG should be briefly indicated
3) The notion and notation of inner product has to be mentioned/ defined before it is used
4) At least in one place, "product" should be replaced by "inner product"
5) Equation (2) should be qualified with: "for fixed M, x and \mathcal{D}"
6) A reference to a paper showing why a MP algorithm is NP-hard should be given.
7) In some cases, pursuit algorithms are globally optimal (in a non-linear approximation sense).
The author should check and reference some papers by Temlyakov.
8) The fact that dictionary elements are normalized should be introduced early on in the paper.
9) It is written "...the procedure concerges to x...", it should actually say that it converges, in general,
in an infinite number of steps (even for discrete settings). Also the reference to the original prrof of convergence should be given.
10) It is written "...its major mathematical aspects was ...". The word "was" should be replaced by "were".
11) What signal is being analyzed in Figure 2? The information displayed in Figure 2 is not clear, one reason, I believe, is that too many issues are addressed at once.
12) Doesn't the Wigner distribution need a brief explanation?
13) I believe the \mathcal{E} in front of equation (7) refers to "energy", if so shouldn't the inner products of the expansion be squared?

I am not familiar with the review process for scholarpedia, I am sure all the information is somewhere in the web site but I would apreciate some guidence from the editor (even if the guidance is automatically generated). In particular, I am not clear if the editor would like from me an opinion on the overall quality of the work. Is the author going to read my full review?

In any case, I believe that if the present paper, which presents a summary of MP, is designed as a pedagogical work, it needs more space to develop the topic in a more clear way.

My comments (and thanks:) to the 1st review:

1) I suggest to intorduce a symbol, say \mathcal{D}, for a generic dictionary earlier on the paper,

-ok

2) The meaning of abreviations such as EEG/MEG should be briefly indicated

-that's linked to relevant sections of Scholarpedia at the first occurence, so I think we can leave it as it is?

3) The notion and notation of inner product has to be mentioned/ defined before it is used

-a proper introduction would I think require separate definitions for discrete and continuous cases, which in this article are mixed for heuristic purposes. That would make this article look even more math-loaded, while I hope it is still accesible also to neuroscientists... I believe that it is quite a basic notion, so we do not have to define everything?

4) At least in one place, "product" should be replaced by "inner product"

-Yes thanks my common error that should also make clearer the previous issue

5) Equation (2) should be qualified with: "for fixed M, x and \mathcal{D}"

-ok

6) A reference to a paper showing why a MP algorithm is NP-hard should be given.

-guidelines say to keep references to minimum; that proof I've seen in the dissertation of Geoff Davis, but instead of adding this I deleted also ref to my own dissertation, and in the text I left only "intractable".

7) In some cases, pursuit algorithms are globally optimal (in a non-linear approximation sense). The author should check and reference some papers by Temlyakov.

-frankly I do not see the relevance of this in biomedical signal processing, which seems to be the topic linking this article to Scholarpedia as I understand. I hope anybody will be able to supplement the article in Wikipedia-like style.

8) The fact that dictionary elements are normalized should be introduced early on in the paper.

-ok

9) It is written "...the procedure concerges to x...", it should actually say that it converges, in general, in an infinite number of steps (even for discrete settings). Also the reference to the original prrof of convergence should be given.

-ok

10) It is written "...its major mathematical aspects was ...". The word "was" should be replaced by "were".

-whole sentence removed

11) What signal is being analyzed in Figure 2? The information displayed in Figure 2 is not clear, one reason, I believe, is that too many issues are addressed at once.

-I replaced this figure

12) Doesn't the Wigner distribution need a brief explanation? 13) I believe the \mathcal{E} in front of equation (7) refers to "energy", if so shouldn't the inner products of the expansion be squared?

-Yes! Thanks a lot

In any case, I believe that if the present paper, which presents a summary of MP, is designed as a pedagogical work, it needs more space to develop the topic in a more clear way.

-space has grown after explaining W-V transform, AFAIR that should be not too big either..

I have gone trhough the answers from Piotr Durka to the comments in my original review. I now understand better the nature of the article and like the final version of the paper. I would suggest to change the title as, as it stands, it may suggest a more thorough presentation. What about the name: "Introduction to Matching Pursuit for Biomedical Signal Analysis"?

I have found two typos in a quick reading:

"Multichannel extension" should be replaced by "Multichannel extensions"

The caption in Figure 6 contains "sam" it should be replaced by "same".

I recommend publication after changing th ename of the article.

IIND RESPONSE OF THE AUTHOR:

Thanks, I corrected these and other typos, as for the title that decision belongs to the Editors--frankly I had a feeling that whole Scholarpedia is neuroscience-related, so such a bias in the article should be expected--but maybe I'm wrong.

the line

"..., biasing other estimates (figure)..." is not clear and the actual figure is not specified.